The present invention relates to electrical induction logging systems for predicting the nature and characteristics of subsurface formations penetrated by a borehole. More particularly, the present invention relates to an improved method for processing electrical signals generated by an induction logging tool, or sonde, to obtain an accurate assessment of the conductivity of the various subsurface formations. Still more particularly, the present invention relates to an improved method for processing the measured signal induced in the receiver coil of the sonde to account for nonlinear variations in the measured signal as a function of variations in the conductivity of formations within a predetermined distance from the sonde.
The production of hydrocarbons from subsurface formations typically commences by forming a borehole through the earth to a subsurface reservoir thought to contain hydrocarbons. As drilling progresses, various physical, chemical, and mechanical properties are "logged" for the purpose of determining the nature and characteristics, including for example, the porosity, permeability, saturation, and depth, of the subsurface formations encountered. One such logging technique commonly used in the industry is referred to as induction logging. Induction logging measures the conductivity or its inverse, the resistivity, of a formation. Formation conductivity is one possible indicator of the presence or absence of a significant accumulation of hydrocarbons because, generally speaking, hydrocarbons are relatively poor conductors of electricity. Formation water, on the other hand, typically salty, is a relatively good conductor of electricity. Thus, induction logging tools can obtain information that, properly interpreted, indicates the presence or absence of hydrocarbons.
U.S. Pat. Nos. 3,056,917; 3,147,429; and 3,179,879 illustrate typical prior-art tools that operate according to the basic principles of induction logging. The downhole tool comprises a transmitter coil and a separate receiver coil wound about a nonconductive mandrel and spaced apart coaxially. A signal generator connected to the transmitter coil produces an alternating current of constant amplitude and frequency within the transmitter coil. The flow of alternating current in the transmitter coil induces a magnetic field within the surrounding formation, causing the flow of eddy currents within the formation circumferentially about the axis of the tool. The eddy currents, in turn, induce a magnetic field that is coupled to the receiver coil, thereby inducing in the receiver coil a voltage signal with magnitude and phase dependent upon the electrical characteristics of the adjacent formation. U.S. Pat. No. 4,302,722 discloses a two-coil tool wherein the transmitter and receiver coils are disposed with their axes generally perpendicular to the borehole axis, for the purpose of facilitating vertical conductivity measurements.
Typically, the signal from the receiver coil is applied to one or more phase detection circuits, each of which generates a signal proportional to the magnitude of that component of the receiver coil signal having a particular, predetermined phase. Thus, one such phase detector circuit senses the magnitude of the component of the receiver coil signal that is in-phase with the transmitter current in the transmitter coil. This component signal is commonly referred to as the real or in-phase (R) component. A second phase detection circuit commonly used in induction logging tools detects the component of the receiver coil signal that is 90 degrees out of phase with the transmitter current. This latter component signal is commonly referred to as the quadrature-phase (X) component signal. Measurement of the R and X phase component signals is well known in the art, as disclosed, for example, in U.S. Pat. Nos. 3,147,429; 4,467,425; and 4,471,436. U.S. Pat. Nos. 4,499,421; 4,499,422; and 4,720,681 disclose more recent apparatus particularly adapted for measuring accurately the R and X signals.
Because the output signal from the receiver coil is not itself an absolute measure of conductivity, but rather is proportional to the true formation conductivity, the output signal must be processed to obtain a log or plot of true formation conductivity as a function of axial depth in the borehole. Most modern theoretical analysis of induction log processing is based upon the work of H. G. Doll, which is summarized in an article, "Introduction to Induction Logging and Application to Logging of Wells Drilled With Oil-Base Mud," published at pages 148-162 in the June 1949 issue of Petroleum Transactions. According to Doll's analysis, the in-phase component of the signal induced in the receiver coil is directly proportional to the conductivity of the surrounding formation, and the constant of proportionality, referred to by Doll as the "geometrical factor," is a function of the geometry of the tool as it relates to the portion of the formation being measured.
Doll calculated what he termed the "unit geometrical factor," which defines the relationship between the conductivity of a so-called "unit ground loop," a horizontal loop of homogeneous ground having a circular shape with its center on the axis of the borehole and having a very small, square cross section, and the elementary voltage signal contributed by the unit ground loop to the total in-phase signal induced in the receiver coil. By integrating the unit geometrical factor across all unit ground loops lying within a horizontal plane spaced at some axial distance z from the center of the coil system, Doll obtained the geometrical factor for a "unit bed." A plot of this geometrical factor as a function of the axial distance from the center of the coil system gives what is commonly referred to as the "vertical geometrical factor" for the tool. It is an accurate plot of the sonde response function relating formation conductivity to output voltage measurements for the tool, assuming no attenuation or phase shift of the induced magnetic field as a consequence of the conductivity of the surrounding formation.
When the formation surrounding the tool is conductive, the electromagnetic field penetrating the formation is attenuated as a consequence of resistive losses through eddy currents induced by the electromagnetic field within the conductor. This "skin effect" tends with increasing conductivity to diminish the magnitude of the in-phase component signal induced in the receiver coil. Thus, in highly conductive formations, the sonde response function relating formation conductivity to measured output signal in the receiver coil is not strictly a function of tool and formation geometry, i.e., the vertical geometrical factor of the tool, but is also a function of the conductivity of the formation. The relationship of the skin-effect phenomenon to the analysis of induction logs is discussed at some length in an article by J. H. Moran and K. S. Kunz, entitled "Basic Theory of Induction Logging and Application to Study of Two-Coil Sondes," published at pages 829-858 of the December 1962 issue of Geophysics (the "Moran article"). In addition, the skin-effect phenomenon is discussed in some detail in U.S. Pat. No. 3,147,429, issued to J. H. Moran, which is hereby incorporated by reference.
The Moran article discloses that the magnitude of the skin effect phenomenon is a complex function of the coil system operating frequency, the spacing between the transmitter and receiver coils, and the conductivity of the adjacent formation material. The article also discloses that the variations introduced by the operating frequency and the conductivity are not linear, which makes it particularly difficult to account for their effects on the sonde response function. By selective choice of operating frequency and coil length, the effect of the skin-effect phenomenon can be minimized or substantially eliminated for a large range of formation conductivity values. See, e.g., U.S. Pat. No. 4,604,581. In many instances, however, these limitations place restraints on the logging system that are not acceptable. Accordingly, for a significant proportion of induction logging activity, it is necessary to account accurately for the nonlinear variations in sonde response function as a consequence of the conductivity of the adjacent formation material.
The Moran article and the Moran patent disclose that the magnitude of the quadrature-phase (X) component of the receiver coil signal gives an approximation of the skin-effect phenomenon. Thus, the Moran patent assumes that the vertical geometrical factor accurately relates the true formation conductivity to the in-phase component of the receiver coil signal for zero conductivity. As conductivity increases, more of the current induced in the receiver coil is phase-shifted and attenuated as a consequence of the skin effect and the magnitude of the in-phase component of the receiver coil signal is diminished as the magnitude of the quadrature-phase component of the receiver coil signal increases. According to the Moran patent, the magnitude of the quadrature-phase component is approximately equal to the magnitude of the skin-effect losses to the in-phase signal. Thus, the Moran patent corrects for the skin-effect phenomenon by adding the real component of the quadrature-phase signal to the real component of the in-phase signal to obtain a measure of the apparent conductivity, which is related to the true formation conductivity by the vertical geometrical factor.
The approach adopted by the Moran patent to account for the skin-effect phenomenon represents a relatively crude approximation based on several assumptions. One such assumption is that the adjacent formation material is homogeneous, with little or no variation in conductivity. Thus, where the formation being measured is a relatively thin bed and the adjoining beds vary significantly in conductivity, Moran's approach would not account accurately for the spacial variations in formation conductivity and their effect on the signal measured in the receiver coil. Likewise, where the adjacent formation is significantly invaded by drilling mud having a conductivity substantially different from that of the invaded formation material, Moran's approach again would not account accurately for the spacial variations in the conductivities. Accordingly, it is necessary in processing the output signal from the receiver coil of an induction logging tool not only to account for the effect of conductivity on the output signal but also to account for variations in conductivity from all parts of the surrounding formation that contribute to the measured signal at any particular axial position within the borehole.
U.S. Pat. Nos. 4,467,425 and 4,471,436 (Schaefer, et al.), which are hereby incorporated herein by reference, disclose more recent efforts to correct for variations in the output signal measured in the receiver coil due to spacial variations resulting from the skin-effect phenomenon. Based on the work of Doll and Moran, Schaefer, et al. derive an expression for the conductivity signal in the receiver coil, assuming no skin effect, as being the convolution of true formation conductivity with a forward transfer function equivalent to the vertical geometrical factor (or sonde response function) for the sonde. The forward transfer function then is modified by means of Fourier analysis to account for changes due to spacial variations in formation conductivity to obtain a spacial domain system response function that maps true formation conductivities into the measured voltages obtained by the sonde. Thus, an approximation of true formation conductivity is obtained by deconvolving the measured signal in the receiver coil with the modified system response function for the sonde.
Schaefer, et al. focus on two problems associated with variations in formation conductivity. The first, or "shoulder effect," is the skew in measured conductivity data for a thin bed of relatively low conductivity caused by eddy currents flowing in adjacent beds having relatively higher conductivities. The unwanted contributions from the adjacent beds result in a measured conductivity in the target thin bed somewhat higher than true. The second problem addressed by Schaefer, et al. is the skin effect phenomenon resulting from attenuation and phase shift of the induced electromagnetic field with increasing conductivity of the formation, as described above.
To compensate for the shoulder effect, Schaefer, et al. construct in the spacial frequency domain a truncated, linear time-invariant filter having a limited frequency response that suppresses signal contributions beyond a predetermined cutoff frequency. The particular filter disclosed is a type of finite-duration, impulse response filter known as a Kaiser window function. By convolving the inverse Fourier transform of this linear filter with the in-phase component of the sonde transfer function at a given conductivity, Schaefer, et al. suppress unwanted conductivity contributions from adjacent beds without affecting the shape of the sonde transfer function within the axial span of the thin bed.
To compensate for the skin-effect attenuation of the in-phase component of the measured voltage in the receiver coil, Schaefer, et al. construct an adaptive spacial filtering function that, when convolved with the quadrature-phase component of the sonde response function, gives an approximation of the magnitude of the skin-effect attenuation. Construction of the adaptive filtering function comprises a two-step process. First, the normalized average of two finite impulse response filters at two separate conductivities is applied to the quadrature-phase component of the sonde response function at all conductivities to fit the quadrature-phase component of the sonde response function to the shape of a function that maps formation conductivity into the real part of the skin-effect error signal. The skin-effect error signal comprises the difference between the real component of the sonde response function at zero conductivity and the in-phase component of the measured conductivity signal. Next, a boosting function is constructed to adjust the magnitude of the transformed quadrature-phase component of the sonde response function to the magnitude of the function that maps formation conductivity into the real part of the skin-effect error signal. This boosting function comprises the ratio of the skin-effect error signal to the quadrature-phase component of the measured conductivity signal When the boosting function has been computed for all conductivities, the values are curve-fitted to obtain the function that best fits the quadrature-phase component of the sonde response function to the skin-effect error function that maps formation conductivity into the real part of the skin-effect error signal.
U.S. Pat. No. 4,604,581 (Thadani, et al.) discloses various techniques for adapting the tool operating frequency to minimize variations in tool response due to skin effect. Thadani, et al. also disclose a deconvolution filter designed to compensate for skin effect, wherein the formation conductivity, as it varies from bed to bed, is modeled as a "staircase" conductivity profile expressed as a weighted linear combination of unit step functions. The deconvolution of the weighted linear unit step combination is constructed using a weighted linear combination of unit step function deconvolutions.
The methods of Schaefer, et al. and Thadani, et al., although improving upon the method of Moran, represent substantially linear, time-invariant approximations of the effect of variable formation conductivities. Like Moran, Schaefer, et al.'s approximation of the skin-effect attenuation is based on the quadrature-phase component signal. Schaefer, et al.'s method improves upon Moran's method by rendering it adaptive to variations between the quadrature-phase component of the receiver coil signal and the real component of the approximated skin-effect error signal. Even so, however, the method of Schaefer, et al. and that of Thadani, et al. do not account for attenuation of the electromagnetic field as it passes through formation material of varying conductivity and do not utilize a system response function that is truly responsive to nonlinear, time-variant changes in formation conductivity. Hence, it would be advantageous to provide a method for processing the output voltage signals from an induction log tool whereby the measured voltage signals are deconvolved with a sonde response function that can account for nonlinear variations in the measured output voltage signal as a consequence of a plurality of different formation conductivities within a predetermined zone surrounding the sonde.